Practice Parallelism in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Lines in the same plane that never intersect because they maintain a constant distance from each other.

Railroad tracks—they stay exactly the same distance apart and never meet, no matter how far they extend.

Example 1

easy
Line \ell_1 passes through (0, 2) and (4, 6). Write the equation of a line \ell_2 parallel to \ell_1 passing through (1, -3).

Example 2

medium
Transversal t crosses parallel lines \ell_1 \parallel \ell_2. If the co-interior (same-side interior) angle at \ell_1 is 65°, find the co-interior angle at \ell_2 and the alternate interior angle at \ell_2.

Example 3

easy
Are the lines y = 3x + 7 and 6x - 2y = 4 parallel? Justify your answer.

Example 4

hard
Parallelogram PQRS has P(0,0), Q(5,0), R(7,4). Find coordinates of S so that PQ \parallel SR and PS \parallel QR.
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